This work deals with a type of non-standard DSW, that for which there is a resonance between the waves of the DSW and
linear, diffractive radiation. This resonance has a major effect on the DSW structure as the resonant radiation leaks mass
and energy from it. The standard example equations governing such resonant DSWs are the Kahawara equation [1]}
\(\frac{\partial w}{\partial t} + 6 w\frac{\partial w}{\partial x} + \mu \frac{\partial ^{3} w}{\partial x^{3}} +\frac{\partial ^{5} w}{\partial x^{5}} = 0\) 
